Statistical mechanics of hyperuniform materials and particle packings

Abstract

In this dissertation, the theoretical machinery of statistical mechanics is applied to investigate hyperuniform materials and particle packings. In the first part of the dissertation (Chapters 2-6), we develop novel methods to generate/construct hyperuniform materials in silico, and study their effective physical properties. Specifically, in Chapters 2 and 3, we develop techniques to design and construct hyperuniform two-phase materials and networks, which can be readily realized by 3D printing and lithographic technologies. We also investigate the effective transport and mechanical properties, and wave-propagation characteristics of these materials. In Chapter 4, we computationally explore the use of

the self-assembly process of binary mixtures of charged colloids in

suspension in order to guide experimentalists to fabricate large samples of

effectively disordered hyperuniform materials in two dimensions. In Chapter 5,

we employ Lloyd's centroidal Voronoi diagram algorithm to solve the Quantizer problem, and obtain universal disordered hyperuniform final states associated with deep local energy minima when starting from random initial conditions. In Chapter 6, we devise techniques to design experimentally realizable

spherical colloidal particles with optimized ``patchy'' anisotropic interactions

for a wide class of 2D target low-coordinated hyperuniform

structures such as square, honeycomb, kagom\'e, and parallelogrammic crystals that are defect-free.

In the second part of the dissertation (Chapters 7-10), we

study how particle shape, size distribution, and container can be used as tuning parameters to achieve a rich diversity of emergent properties of particle packings, and develop packing models for real biological systems. In Chapter 7, we ascertain with high precision the stable phases of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. We also determine the density of jammed (mechanically stable) states with maximal disorder of this system, which in some sense can be regarded to be a prototypical glass. In Chapter 8, we examine disordered jammed binary sphere packings that are confined between two parallel hard planes, which possess packing characteristics that are substantially different from their bulk analogs. In Chapter 9, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin, and construct a statistical-mechanical model of packings of epithelial cells at late developmental stage. In Chapter 10, we use our knowledge of particle packings to devise a predictive computational model to probe the conditions surrounding tumor dormancy and the ``switch'' to malignant states.